We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations that arise in presence of discontinuities when high order spatial discretizations are employed. This goal is achieved using a filter function that keeps the high order scheme when the solution is regular and switches to a monotone low order approximation if it is not. The method has been implemented in the framework of the $deal.II$ numerical library, whose mesh adaptation capabilities are also used to reduce the region in which the low order approximation is used. A number of numerical experiments demonstrate the potential of the proposed filtering technique.

翻译：我们引入了一种过滤技术, 用于对双曲问题不连续的加列尔金近似值进行过滤。 按照其他作者已经为汉密尔顿- 雅科比等式提议的一种方法, 我们的目标是减少在使用高顺序空间离散时出现不连续时产生的虚假振荡。 实现这一目标时使用了过滤功能, 即当解决方案是常规的时保持高排序, 如果不是常规的, 则切换到单质低排序近似值。 这种方法是在 $deal. II$ 数字图书馆的框架内实施的, 后者的网状适应能力也被用于减少使用低顺序近似值的区域。 一些数字实验显示了拟议的过滤技术的潜力 。